Division bar
A division bar acts as both a division symbol and a grouping symbol, meaning you must simplify the expressions above and below the bar before dividing. For example, (4 + 5 x 6 - 7) / (10 - (9 - 8)) becomes (4 + 30 - 7) / (10 - 1) = 27/9 = 3. This concept is covered in Chapter 7 of Saxon Math Course 2 for 7th grade math and teaches students to treat the numerator and denominator of a fraction as separate grouped expressions, a skill essential for algebra and evaluating complex numerical expressions.
Key Concepts
Property A division bar can serve as a symbol of inclusion. We simplify above and below the division bar before we divide.
Examples $\frac{4 + 5 \times 6 7}{10 (9 8)} = \frac{4 + 30 7}{10 1} = \frac{27}{9} = 3$ $\frac{10 + 9 \cdot 8 7}{6 \cdot 5 4 \cdot 3 + 2} = \frac{10 + 72 7}{30 12 + 2} = \frac{75}{20} = \frac{15}{4}$.
Explanation Treat the numerator and the denominator as two separate mini problems. You need to completely solve the top expression and the bottom expression first. Only when you have a single number on top and a single number on bottom can you perform the final, epic division!
Common Questions
What is a division bar in math?
A division bar is the horizontal line in a fraction that separates the numerator from the denominator. It serves as both a division sign and a grouping symbol, telling you to evaluate the top and bottom expressions completely before dividing.
How do you simplify expressions with a division bar?
First, simplify the entire numerator using order of operations. Then simplify the entire denominator. Finally, divide. For (4 + 5 x 6 - 7)/(10 - (9 - 8)): top = 4 + 30 - 7 = 27, bottom = 10 - 1 = 9, answer = 27/9 = 3.
Why is a division bar considered a symbol of inclusion?
Because it groups everything above it and everything below it separately, just like parentheses group terms inside them. You must treat the numerator and denominator as if they each have invisible parentheses around them.
How do you apply order of operations with a division bar?
Apply PEMDAS separately to the numerator and denominator. Evaluate exponents, then multiplication and division left to right, then addition and subtraction left to right within each part. Only divide the final simplified numerator by the final simplified denominator.
What is a common mistake with division bar problems?
Students often try to simplify across the bar instead of completing the top and bottom separately first. For example, in (10 + 6)/4, you cannot cancel the 10 with 4. You must add 10 + 6 = 16 first, then divide 16/4 = 4.
When do students learn about the division bar as a grouping symbol?
This concept is taught in 7th grade math. Saxon Math Course 2 covers it in Chapter 7 as part of a broader lesson on symbols of inclusion, helping students handle complex fraction expressions.